To estimate the volume of Natasha's toy chest, we start by considering the dimensions provided: 50 inches in length, 20 inches in width, and 20 inches in height.
1. Identify Dimensions:
- Length: 50 inches
- Width: 20 inches
- Height: 20 inches
2. Volume Calculation:
Using the formula for the volume of a rectangular prism (which is also applicable to this toy chest), we calculate the volume as follows:
[tex]\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
\][/tex]
3. Substitute the Given Values:
[tex]\[
\text{Volume} = 50\, \text{inches} \times 20\, \text{inches} \times 20\, \text{inches}
\][/tex]
4. Perform the Multiplication:
- First multiply the width and height: [tex]\(20 \times 20 = 400\)[/tex]
- Then multiply the result by the length: [tex]\(50 \times 400 = 20000\)[/tex]
Therefore, the volume of the toy chest is:
[tex]\[
20000\, \text{in}^3
\][/tex]
5. Select the Closest Estimate:
Given the options:
- [tex]\(2 \times 10^3\)[/tex] in[tex]\(^3\)[/tex]
- [tex]\(2 \times 10^4\)[/tex] in[tex]\(^3\)[/tex]
- [tex]\(2 \times 10^5\)[/tex] in[tex]\(^3\)[/tex]
- [tex]\(2 \times 10^6\)[/tex] in[tex]\(^3\)[/tex]
The volume we calculated (20000 in[tex]\(^3\)[/tex]) matches [tex]\(2 \times 10^4\)[/tex] in[tex]\(^3\)[/tex].
Hence, the best estimate that approximates the volume of the toy chest is:
[tex]\[
2 \times 10^4 \, \text{in}^3
\][/tex]
